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Properties of product preserving functors

Gancarzewicz, Jacek, Mikulski, Włodzimierz, Pogoda, Zdzisław (1994)

Proceedings of the Winter School "Geometry and Physics"

A product preserving functor is a covariant functor $ℱ$ from the category of all manifolds and smooth mappings into the category of fibered manifolds satisfying a list of axioms the main of which is product preserving: $ℱ (M_{1} \times M_{2}) = ℱ (M_{1}) \times ℱ (M_{2})$ . It is known that any product preserving functor $ℱ$ is equivalent to a Weil functor $T^{A}$ . Here $T^{A} (M)$ is the set of equivalence classes of smooth maps $ϕ : ℝ^{n} \to M$ and $ϕ, ϕ^{'}$ are equivalent if and only if for every smooth function $f : M \to ℝ$ the formal Taylor series at 0 of $f \circ ϕ$ and $f \circ ϕ^{'}$ are equal in $A = ℝ [[x_{1}, \dots, x_{n}]] / 𝔞$ . In this paper all...

Proximity and construction of compactifications with given properties

Smirnov, Yu. M. (1967)

General Topology and its Relations to Modern Analysis and Algebra

Proximity approach to topological problems

Gagrat, M., Naimpally, S. A. (1972)

General Topology and its Relations to Modern Analysis and Algebra

$Q$ -curvature and spectral invariants

Branson, Thomas (2005)

Proceedings of the 24th Winter School "Geometry and Physics"

$q$ -deformed inverse scattering problem

Hrubý, J. (1994)

Proceedings of the Winter School "Geometry and Physics"

Summary: Starting from the physical point of view on the Miura transformation as reflectionless potential and its connection with supersymmetry we define a scaling $q$ -deformation of this to obtain $q$ -deformed supersymmetric quantum mechanics. An application to an inverse scattering problem is given.

$q$ -difference conformal invariant operators and equations

Dobrev, V. K. (1996)

Proceedings of the 15th Winter School "Geometry and Physics"

QCD at the hadron scale and non-local Thirring model

Souček, Jiří (1987)

Proceedings of the Winter School "Geometry and Physics"

Quantum deformation of relativistic supersymmetry

Sobczyk, Jan (1996)

Proceedings of the 15th Winter School "Geometry and Physics"

From the text: The author reviews recent research on quantum deformations of the Poincaré supergroup and superalgebra. It is based on a series of papers (coauthored by P. Kosiński, J. Lukierski, P. Maślanka and A. Nowicki) and is motivated by both mathematics and physics. On the mathematical side, some new examples of noncommutative and noncocommutative Hopf superalgebras have been discovered. Moreover, it turns out that they have an interesting internal structure of graded bicrossproduct. As far...